%------------------------------------------------------------------------------
% File : CSE_E---1.7
% Problem : GRP060-1 : TPTP v9.2.1. Released v1.0.0.
% Transfm : none
% Format : tptp:raw
% Command : /export/starexec/sandbox2/solver/bin/lemma_parallel_prover %s --lemma-prover /export/starexec/sandbox2/solver/bin/cse --final-prover /export/starexec/sandbox2/solver/bin/eprover --proof-time %d --global-time-limit %d
% Computer : n008.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Tue May 5 04:23:42 PM UTC 2026
% Result : Unsatisfiable 4.15s 3.28s
% Output : CNFRefutation 4.15s
% Verified :
% SZS Type : Refutation
% Derivation depth : 33
% Number of leaves : 2
% Syntax : Number of clauses : 57 ( 54 unt; 0 nHn; 5 RR)
% Number of literals : 62 ( 61 equ; 9 neg)
% Maximal clause size : 3 ( 1 avg)
% Maximal term depth : 11 ( 3 avg)
% Number of predicates : 2 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 9 ( 9 usr; 7 con; 0-2 aty)
% Number of variables : 183 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(single_axiom,axiom,
multiply(X1,inverse(multiply(X2,multiply(X3,multiply(multiply(inverse(X3),inverse(multiply(X4,X2))),X1))))) = X4,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',single_axiom) ).
cnf(prove_these_axioms,negated_conjecture,
( multiply(inverse(a1),a1) != multiply(inverse(b1),b1)
| multiply(multiply(inverse(b2),b2),a2) != a2
| multiply(multiply(a3,b3),c3) != multiply(a3,multiply(b3,c3)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_these_axioms) ).
cnf(c_0_2,axiom,
multiply(X1,inverse(multiply(X2,multiply(X3,multiply(multiply(inverse(X3),inverse(multiply(X4,X2))),X1))))) = X4,
single_axiom ).
cnf(c_0_3,plain,
multiply(X1,inverse(multiply(multiply(X2,multiply(multiply(inverse(X2),inverse(multiply(X3,X4))),inverse(X5))),multiply(X5,multiply(X3,X1))))) = X4,
inference(spm,[status(thm)],[c_0_2,c_0_2]) ).
cnf(c_0_4,plain,
multiply(X1,inverse(multiply(multiply(X2,multiply(X3,inverse(X4))),multiply(X4,multiply(X5,X1))))) = multiply(X6,multiply(multiply(inverse(X6),inverse(multiply(X3,X5))),inverse(X2))),
inference(spm,[status(thm)],[c_0_2,c_0_3]) ).
cnf(c_0_5,plain,
multiply(inverse(X1),inverse(multiply(X2,multiply(X3,inverse(multiply(multiply(X1,multiply(X4,inverse(X5))),multiply(X5,multiply(X2,X3)))))))) = X4,
inference(spm,[status(thm)],[c_0_2,c_0_4]) ).
cnf(c_0_6,plain,
multiply(inverse(X1),inverse(multiply(multiply(inverse(X2),inverse(multiply(X3,multiply(X1,multiply(X4,inverse(X2)))))),X3))) = X4,
inference(spm,[status(thm)],[c_0_5,c_0_2]) ).
cnf(c_0_7,plain,
multiply(X1,inverse(multiply(X2,multiply(X3,multiply(X4,X1))))) = multiply(inverse(X5),inverse(multiply(X2,multiply(X3,multiply(X4,inverse(X5)))))),
inference(spm,[status(thm)],[c_0_2,c_0_6]) ).
cnf(c_0_8,plain,
multiply(X1,multiply(multiply(inverse(X1),inverse(multiply(multiply(inverse(X2),inverse(multiply(X3,X4))),X3))),inverse(X2))) = X4,
inference(spm,[status(thm)],[c_0_3,c_0_4]) ).
cnf(c_0_9,plain,
multiply(X1,inverse(multiply(inverse(multiply(X2,multiply(X3,multiply(multiply(inverse(X3),inverse(multiply(X4,X2))),X5)))),multiply(X6,multiply(multiply(inverse(X6),inverse(X4)),X1))))) = X5,
inference(spm,[status(thm)],[c_0_2,c_0_2]) ).
cnf(c_0_10,plain,
multiply(inverse(X1),inverse(multiply(multiply(X2,inverse(multiply(X3,multiply(X1,multiply(X4,X2))))),X3))) = X4,
inference(spm,[status(thm)],[c_0_6,c_0_7]) ).
cnf(c_0_11,plain,
multiply(X1,multiply(multiply(inverse(X1),inverse(X2)),inverse(X3))) = multiply(X4,multiply(multiply(inverse(X4),inverse(X2)),inverse(X3))),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_8,c_0_9]),c_0_2]) ).
cnf(c_0_12,plain,
multiply(inverse(X1),inverse(multiply(multiply(inverse(X2),inverse(multiply(X3,multiply(X4,multiply(multiply(inverse(X4),inverse(X5)),inverse(X2)))))),X3))) = multiply(inverse(X1),inverse(X5)),
inference(spm,[status(thm)],[c_0_10,c_0_11]) ).
cnf(c_0_13,plain,
multiply(X1,inverse(multiply(X2,multiply(X3,multiply(X4,X1))))) = multiply(X5,inverse(multiply(X2,multiply(X3,multiply(X4,X5))))),
inference(spm,[status(thm)],[c_0_7,c_0_7]) ).
cnf(c_0_14,plain,
multiply(X1,inverse(multiply(multiply(X2,multiply(multiply(inverse(X2),inverse(X3)),inverse(X4))),multiply(X4,multiply(X5,X1))))) = inverse(multiply(multiply(X6,multiply(multiply(inverse(X6),inverse(multiply(X7,X3))),inverse(X8))),multiply(X8,multiply(X7,X5)))),
inference(spm,[status(thm)],[c_0_3,c_0_3]) ).
cnf(c_0_15,plain,
inverse(multiply(multiply(inverse(X1),inverse(multiply(X2,multiply(X3,multiply(multiply(inverse(X3),inverse(X4)),inverse(X1)))))),X2)) = inverse(X4),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_3,c_0_12]),c_0_3]) ).
cnf(c_0_16,plain,
multiply(X1,multiply(X2,inverse(multiply(multiply(X3,multiply(multiply(inverse(X3),inverse(X4)),inverse(X5))),multiply(X5,multiply(X1,X2)))))) = X4,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_13,c_0_14]),c_0_3]) ).
cnf(c_0_17,plain,
inverse(multiply(multiply(X1,inverse(multiply(X2,multiply(X3,multiply(multiply(inverse(X3),inverse(X4)),X1))))),X2)) = inverse(X4),
inference(spm,[status(thm)],[c_0_15,c_0_13]) ).
cnf(c_0_18,plain,
multiply(multiply(X1,inverse(multiply(X2,multiply(X3,multiply(multiply(inverse(X3),inverse(X4)),X1))))),X2) = X4,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_16,c_0_17]),c_0_16]) ).
cnf(c_0_19,plain,
inverse(multiply(multiply(inverse(X1),inverse(multiply(X2,X3))),X2)) = inverse(multiply(multiply(inverse(X1),inverse(multiply(X4,X3))),X4)),
inference(spm,[status(thm)],[c_0_17,c_0_8]) ).
cnf(c_0_20,plain,
multiply(X1,inverse(multiply(multiply(X2,multiply(multiply(inverse(X2),inverse(X3)),inverse(X4))),multiply(X4,X3)))) = X1,
inference(spm,[status(thm)],[c_0_2,c_0_18]) ).
cnf(c_0_21,plain,
inverse(multiply(multiply(inverse(X1),inverse(X2)),X2)) = inverse(multiply(multiply(inverse(X1),inverse(X3)),X3)),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_19,c_0_20]),c_0_20]) ).
cnf(c_0_22,plain,
multiply(X1,multiply(inverse(X1),inverse(X2))) = multiply(X3,multiply(inverse(X3),inverse(X2))),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_11,c_0_20]),c_0_20]) ).
cnf(c_0_23,plain,
multiply(multiply(inverse(X1),inverse(X2)),X2) = multiply(multiply(inverse(X1),inverse(X3)),X3),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_16,c_0_21]),c_0_16]) ).
cnf(c_0_24,plain,
multiply(X1,inverse(X1)) = multiply(X2,inverse(X2)),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_22,c_0_20]),c_0_20]) ).
cnf(c_0_25,plain,
multiply(multiply(inverse(X1),inverse(X2)),X2) = multiply(multiply(X3,inverse(X3)),inverse(X1)),
inference(spm,[status(thm)],[c_0_23,c_0_24]) ).
cnf(c_0_26,plain,
multiply(X1,inverse(X1)) = multiply(multiply(inverse(multiply(X2,inverse(X2))),inverse(X3)),X3),
inference(spm,[status(thm)],[c_0_24,c_0_25]) ).
cnf(c_0_27,plain,
multiply(multiply(X1,X2),inverse(multiply(X2,multiply(multiply(X3,inverse(X3)),multiply(X4,inverse(X4)))))) = X1,
inference(spm,[status(thm)],[c_0_2,c_0_26]) ).
cnf(c_0_28,plain,
multiply(X1,inverse(X1)) = multiply(multiply(X2,inverse(X2)),multiply(X3,inverse(X3))),
inference(spm,[status(thm)],[c_0_24,c_0_27]) ).
cnf(c_0_29,plain,
multiply(multiply(X1,X2),inverse(multiply(X2,multiply(X3,inverse(X3))))) = X1,
inference(spm,[status(thm)],[c_0_27,c_0_28]) ).
cnf(c_0_30,plain,
multiply(multiply(X1,multiply(X2,inverse(X2))),inverse(multiply(X3,inverse(X3)))) = X1,
inference(spm,[status(thm)],[c_0_29,c_0_28]) ).
cnf(c_0_31,plain,
multiply(X1,multiply(X2,inverse(X2))) = X1,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_30,c_0_20]),c_0_20]) ).
cnf(c_0_32,plain,
multiply(multiply(X1,X2),inverse(X2)) = X1,
inference(rw,[status(thm)],[c_0_29,c_0_31]) ).
cnf(c_0_33,plain,
multiply(inverse(multiply(X1,multiply(X2,multiply(multiply(inverse(X2),inverse(multiply(X3,X1))),X4)))),inverse(multiply(multiply(X5,multiply(multiply(inverse(X5),inverse(multiply(X4,X6))),inverse(X7))),multiply(X7,X3)))) = X6,
inference(spm,[status(thm)],[c_0_3,c_0_2]) ).
cnf(c_0_34,plain,
multiply(X1,inverse(inverse(X2))) = multiply(X1,X2),
inference(spm,[status(thm)],[c_0_32,c_0_32]) ).
cnf(c_0_35,plain,
inverse(multiply(X1,multiply(X2,multiply(multiply(inverse(X2),inverse(multiply(multiply(X3,X4),X1))),X3)))) = X4,
inference(spm,[status(thm)],[c_0_20,c_0_33]) ).
cnf(c_0_36,plain,
inverse(inverse(X1)) = X1,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_9,c_0_34]),c_0_9]) ).
cnf(c_0_37,plain,
multiply(X1,multiply(inverse(X1),X2)) = multiply(X3,multiply(inverse(X3),X2)),
inference(spm,[status(thm)],[c_0_22,c_0_35]) ).
cnf(c_0_38,plain,
multiply(X1,multiply(inverse(X2),X2)) = X1,
inference(spm,[status(thm)],[c_0_31,c_0_36]) ).
cnf(c_0_39,plain,
multiply(X1,multiply(inverse(X1),X2)) = X2,
inference(spm,[status(thm)],[c_0_37,c_0_38]) ).
cnf(c_0_40,plain,
multiply(multiply(X1,inverse(X2)),X2) = multiply(multiply(X1,inverse(X3)),X3),
inference(spm,[status(thm)],[c_0_23,c_0_35]) ).
cnf(c_0_41,plain,
multiply(inverse(X1),multiply(X1,X2)) = X2,
inference(spm,[status(thm)],[c_0_39,c_0_36]) ).
cnf(c_0_42,plain,
multiply(multiply(X1,inverse(X2)),X2) = multiply(multiply(X3,inverse(X3)),X1),
inference(spm,[status(thm)],[c_0_25,c_0_35]) ).
cnf(c_0_43,plain,
multiply(multiply(X1,inverse(X2)),X2) = X1,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_40,c_0_36]),c_0_32]) ).
cnf(c_0_44,plain,
inverse(multiply(multiply(X1,X2),multiply(X3,multiply(inverse(X3),X4)))) = multiply(multiply(inverse(X4),inverse(X2)),inverse(X1)),
inference(spm,[status(thm)],[c_0_35,c_0_20]) ).
cnf(c_0_45,plain,
multiply(X1,inverse(multiply(X2,X1))) = inverse(X2),
inference(spm,[status(thm)],[c_0_32,c_0_41]) ).
cnf(c_0_46,plain,
multiply(multiply(X1,inverse(X1)),X2) = X2,
inference(rw,[status(thm)],[c_0_42,c_0_43]) ).
cnf(c_0_47,plain,
inverse(multiply(X1,multiply(inverse(X1),multiply(inverse(inverse(multiply(X2,X3))),X4)))) = multiply(multiply(inverse(X4),inverse(X3)),inverse(X2)),
inference(spm,[status(thm)],[c_0_44,c_0_37]) ).
cnf(c_0_48,plain,
multiply(inverse(X1),inverse(X2)) = inverse(multiply(X2,X1)),
inference(spm,[status(thm)],[c_0_41,c_0_45]) ).
cnf(c_0_49,negated_conjecture,
( multiply(inverse(a1),a1) != multiply(inverse(b1),b1)
| multiply(multiply(inverse(b2),b2),a2) != a2
| multiply(multiply(a3,b3),c3) != multiply(a3,multiply(b3,c3)) ),
prove_these_axioms ).
cnf(c_0_50,plain,
multiply(multiply(inverse(X1),X1),X2) = X2,
inference(spm,[status(thm)],[c_0_46,c_0_36]) ).
cnf(c_0_51,plain,
inverse(multiply(multiply(X1,X2),X3)) = inverse(multiply(X1,multiply(X2,X3))),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_47,c_0_36]),c_0_39]),c_0_48]),c_0_48]) ).
cnf(c_0_52,negated_conjecture,
( multiply(multiply(a3,b3),c3) != multiply(a3,multiply(b3,c3))
| multiply(inverse(a1),a1) != multiply(inverse(b1),b1) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_49,c_0_50])]) ).
cnf(c_0_53,plain,
multiply(multiply(X1,X2),X3) = multiply(X1,multiply(X2,X3)),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_36,c_0_51]),c_0_36]) ).
cnf(c_0_54,negated_conjecture,
multiply(inverse(a1),a1) != multiply(inverse(b1),b1),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_52,c_0_53])]) ).
cnf(c_0_55,plain,
multiply(X1,inverse(X1)) = multiply(inverse(X2),X2),
inference(spm,[status(thm)],[c_0_24,c_0_36]) ).
cnf(c_0_56,negated_conjecture,
$false,
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_54,c_0_55]),c_0_55]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : GRP060-1 : TPTP v9.2.1. Released v1.0.0.
% 0.00/0.12 % Command : /export/starexec/sandbox2/solver/bin/lemma_parallel_prover %s --lemma-prover /export/starexec/sandbox2/solver/bin/cse --final-prover /export/starexec/sandbox2/solver/bin/eprover --proof-time %d --global-time-limit %d
% 0.16/0.33 % Computer : n008.cluster.edu
% 0.16/0.33 % Model : x86_64 x86_64
% 0.16/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.16/0.33 % Memory : 8042.1875MB
% 0.16/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.16/0.33 % CPULimit : 300
% 0.16/0.33 % WCLimit : 300
% 0.16/0.33 % DateTime : Mon May 4 18:19:13 EDT 2026
% 0.16/0.33 % CPUTime :
% 0.16/0.34 % start to proof: theBenchmark
% 4.15/3.28 % Version : CSE_E---1.7
% 4.15/3.28 % Problem : theBenchmark.p
% 4.15/3.28 % SZS status Unsatisfiable for theBenchmark.p
% 4.15/3.28 % SZS output start CNFRefutation
% See solution above
% 4.15/3.29 % Total time : 2.373s
%------------------------------------------------------------------------------